Question

I need to prove that A⊂B⇒(A∪C)⊂(B∪C).
Any ideas ?

Answer 1

this ...

\[A\subset B \Rightarrow (A \cup C)\subset (B\cup C)\]?

Answer 2

yes.

Answer 3

let \(x\in A\cup C\). then \(x\in A\) or \(x\in C\)

if \(x\in A\) then \(x\in B\). Hence \(x\in B\cup C\)

if \(x\in C\) then \(x\in B\cup C\)

therefore \(A\cup C\subset B\cup C\)

Answer 4

Thank you very much for your answer ^^